Influence of departures from LTE on determinations of the sulfur abundances in A-K type stars

K. O. Kiselev; S. A. Korotin

REVIEW 3 major objections 4 minor 43 references

Influence of departures from LTE on determinations of the sulfur abundances in A-K type stars

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A revised neutral sulfur model gives consistent sulfur abundances in 13 stars across 4000 to 10000 K, regardless of how strongly individual lines deviate from LTE.

desk verdict A useful incremental update to the sulfur non-LTE grid with a better atomic model and H-band coverage, but the low-gravity end is untested extrapolation and the optical gf tuning is partly circular. read the letter →

arxiv 2501.00774 v1 pith:MESXFRD3 submitted 2025-01-01 astro-ph.SR

S. A. Korotin , K. O. Kiselev This is my paper · ORCID

classification astro-ph.SR

keywords sulfurabundancenon-LTEstellaratmospheresA-typestarsK-typeoscillatorstrengthsinfraredspectroscopyatomicmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that a renewed atomic model for neutral sulfur, using quantum-mechanical collision rates and including ionized sulfur levels, can describe sulfur line formation in stellar atmospheres from 4000 to 10000 K. On 13 well-studied A-K stars, the model fits S I lines from different multiplets with essentially the same sulfur abundance even when those lines are affected very differently by departures from local thermodynamic equilibrium. The authors also present a grid of non-LTE corrections for S I lines in the visible, near-infrared, and H-band regions, together with refined wavelengths and oscillator strengths. If the claim holds, sulfur abundances derived from weak optical lines and from strongly non-LTE infrared triplets can be placed on a common scale, which matters for using sulfur as an alpha-element tracer of galactic chemical evolution.

What carries the argument

The central object is a 64-level neutral sulfur atom augmented by 81 levels of ionized sulfur, the ground level of doubly ionized sulfur, and auxiliary levels treated in LTE, with 775 bound-bound and 146 bound-free transitions. Collisional data come from detailed quantum-mechanical electron-impact rates for the lowest 17 S I levels and hydrogen-impact rates for 40 levels, replacing the earlier approximate formulas. Statistical equilibrium and radiative transfer are solved with a modified non-LTE atmosphere code using opacity distribution functions, and the resulting population ratios are passed to a synthetic-spectrum code to compute line profiles. The correction grid is built by adjusting the sulfur abundance until the non-LTE equivalent width matches the LTE value at each grid point.

What would settle it

For a metal-poor giant with effective temperature 6000 K, surface gravity $\log g=2$, and $[\mathrm{Fe/H}]=-1$, the new model predicts a non-LTE correction of about -0.75 dex for the 9212 Å line, whereas the old model gives -0.85 dex and an earlier independent calculation gives -1.02 dex; a high-resolution, high-S/N spectrum of such a star that yields a sulfur abundance from 9212 Å differing from the 8694 Å or 6757 Å lines by more than the stated uncertainties would contradict the model. A laboratory measurement of the multiplet 6, 8, and 10 oscillator strengths that disagrees with the refined values by more than the quoted adjustments would likewise falsify the solar-calibration assumption.

Watch

Extended reading notes

Core claim

With the updated sulfur model, all observed S I lines in each test star are reproduced with a single sulfur abundance, whether the line forms nearly in LTE or is strongly affected by non-LTE effects. For the two A-type stars, abundances derived from S II lines agree with those from S I lines to within 0.04 dex, which the authors take as evidence that the model is applicable up to at least 10000 K. The accompanying grid of non-LTE corrections covers effective temperatures 4000-10000 K, surface gravities $\log g$ from 0 to 5, and metallicities $[\mathrm{Fe/H}]$ from 0 to -2, and it replaces earlier approximate collision data with detailed quantum-mechanical rates.

Load-bearing premise

The solar-calibrated oscillator strengths and the adopted literature stellar parameters are assumed to transfer to all 13 program stars, so if the oscillator-strength adjustments absorb model errors or do not transfer, the claimed abundance consistency is partly built in by construction.

Editorial extensions

If this is right

Users can apply the published grid to correct LTE sulfur abundances for S I lines across the full 4000-10000 K range, including H-band lines around 1.5-2.3 microns that earlier grids did not cover.
For dwarf stars, multiplet 8 at 6743-6757 Å and multiplet 10 at 6046-6052 Å have near-zero non-LTE corrections and can be used in LTE analysis, while the 9212-9237 Å and 10455-10459 Å triplets require non-LTE corrections that reach several tenths of a dex.
The refined wavelengths and oscillator strengths for multiplets 6, 8, 10 and the infrared H-band lines provide a recommended S I line list for abundance work.
Agreement between S I and S II abundances in two 9600 K stars extends the validity of the model from cool K stars to A-type stars, so sulfur can be measured in hotter stars with the same atomic model.
For metal-poor giants, the new quantum-mechanical hydrogen collision rates give smaller departures from LTE than the old approximate-formula model, changing derived abundances by roughly 0.1 dex for lines like 9212 Å.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the correction grid is immediately testable against large stellar surveys of metal-poor stars, where the disputed [S/Fe] plateau below [Fe/H] = -2 could be re-examined with a homogeneous non-LTE treatment.
Beyond the paper: if future laboratory measurements confirm the adjusted oscillator strengths for multiplets 6, 8, and 10, the solar calibration is independently validated; if laboratory values disagree, part of the abundance consistency may be an artifact of absorbing model error into the line parameters.
Beyond the paper: the model's structure suggests a natural next test--applying it to warmer A-type stars beyond 10000 K where S II lines dominate and checking whether S I and S II abundances continue to agree, which would probe the ionization balance and the coupling to doubly ionized sulfur.
Beyond the paper: the reported non-LTE correction depends on microturbulent velocity for strong lines, so grid users should recompute individual corrections for giants with large microturbulence rather than interpolating blindly.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a genuinely useful update of the sulfur non-LTE correction grid, and the validation is decent for the parameter range actually tested. The weak spot is that the grid is advertised for log g = 0–5 but every validation star sits at log g ≥ 2.32, so the most extreme corrections are pure extrapolation.

What's new: the authors replace the Drawin-formula and approximate electron rates with quantum-mechanical rates (Belyaev & Voronov 2020, ADAS), add S II levels to push the model to 10000 K, add H-band lines, and refine wavelengths and gf's for several multiplets. The grid is a real extension of Korotin 2009, not a re-badging. The best evidence is the solar IR-triplet fit: using measured oscillator strengths from Zerne et al., they get 7.16 against the meteoritic 7.15, with no tuning. That is an independent success. The 13-star multi-line consistency is also a meaningful test, though less clean because the optical gf's were solar-tuned.

Where it's soft: the low-gravity regime is exactly where the corrections are largest (approaching –1 dex or more) and where hydrogen collisions dominate, and there is no observed spectrum below log g = 2.32. The solar calibration cannot cover this because the Sun is a dwarf. This does not invalidate the model, but it means the grid's most extreme entries are unsupported extrapolation. A referee should ask for at least one low-gravity benchmark (e.g., a well-studied supergiant) or a clear statement that the low-log g corrections are provisional. Also, the quoted errors are line-to-line scatter only; systematic uncertainties from gf adjustments and stellar parameters are not quantified. The paper excludes several awkward lines, which is defensible but should be explicit.

Who it's for: stellar abundance practitioners working on A–K stars, especially those with IR spectra. It deserves peer review; with the low-gravity caveat and a proper error budget it can become a standard reference. I would take the grid seriously, with caution at low gravity.

Referee Report

3 major / 4 minor

Summary. The paper presents an updated non-LTE atomic model for neutral sulfur and a grid of non-LTE abundance corrections for S I lines in the visible and infrared, including the H-band, for effective temperatures 4000-10000 K, log g 0-5, and [Fe/H] 0 to -2. The model incorporates quantum-mechanical inelastic collision rates with electrons (ADAS) and hydrogen (Belyaev & Voronov 2020), adds S II and S III levels to handle higher temperatures, and is tested by fitting S I and S II lines in 13 stars with well-determined parameters. The authors refine the wavelengths and oscillator strengths of several S I multiplets using the solar spectrum, propose a recommended line list, and compare their correction grid with earlier non-LTE calculations.

Significance. If the results hold, the model and correction grid provide a modern, practical tool for sulfur abundance determinations in A-K stars, with genuinely improved input physics. The strongest evidence is the solar fit of the 10455-10459 Å IR triplet using laboratory-measured oscillator strengths at (S/H)=7.16, and the S I/S II agreement in the two A-type stars. The multi-line, multi-star consistency test is a meaningful relative test of the non-LTE calculations. The electronic correction grid is a useful community resource. However, the absolute scale of the visible and H-band analyses is tied to the meteoritic solar abundance by construction, and the low-gravity portion of the grid is not covered by any of the 13 test stars; both points limit the strength of the validation as stated.

major comments (3)

[Section 3, Table 1, Section 5] The oscillator strengths for multiplets 6, 8, and 10 and for the H-band lines are adjusted so that solar synthetic profiles match the adopted meteoritic sulfur abundance (log gf ZB +0.088 for multiplet 6, +0.075 for multiplet 8, +0.113 for multiplet 10, and BQZ -0.12 for the 15400 Å multiplets). Consequently, the agreement of these lines with the solar spectrum is partly built in and cannot serve as an independent validation of the absolute abundance scale; only the 10455-10459 Å triplet, with oscillator strengths measured by Zerne et al. (1997), provides an independent solar test. The 13-star consistency check then uses the solar-calibrated gf values, so it tests the transferability of the calibration and the non-LTE corrections, but not the absolute zero point. The authors should make this distinction explicit, quote uncertainties for the fitted gf offsets, and demonstrate quantitatively that the offsets lie within the mutual scatter of the theoretical sources (ZB, BQZ, DH), as the text currently suggests but does not document.
[Section 6, Table 2, Figs. 7-11] The grid is claimed for log g 0-5, but all 13 test stars have log g greater than or equal to 2.32 (Table 2; HD 195295 has log g=2.32). The largest non-LTE corrections occur precisely in the low-gravity regime (log g=0-1), where the corrections for the IR triplet reach magnitudes of order -1 dex, whereas the most non-LTE-sensitive test star shows corrections only down to about -0.8 dex. The solar calibration in Section 3 cannot test this regime because the Sun has log g=4.44 and H-impact collisions are far less influential there. Thus the most extreme entries of the correction grid are validated only by extrapolation from dwarfs and moderate giants. The authors should either analyze spectra of low-gravity giants or supergiants with log g below about 2, or explicitly state that grid entries below log g approximately 2 are extrapolations that require individual non-LTE calculations.
[Section 4.1, Table 2] The quoted uncertainties are only the line-to-line scatter of the fitted abundances. Systematic errors from the adopted stellar parameters (Jofré et al. 2015; Lyubimkov et al. 2010), from the roughly 0.1-0.3 dex uncertainty in the oscillator-strength sources, and from continuum placement are not propagated. Since the paper's central claim is that lines with very different non-LTE corrections yield similar abundances, a quantitative sensitivity analysis is needed to show that the scatter among lines and stars is compatible within the full error budget. For example, the authors should report abundance variations for perturbations of Delta Teff=+-100 K, Delta log g=+-0.2, Delta [Fe/H]=+-0.1, and Delta Vt=+-0.2 km/s, and for choosing ZB, BQZ, or DH gf values rather than their adopted offsets.

minor comments (4)

[Abstract, Section 4.1] The statement that sulfur lines in all test stars are fitted with similar abundances is stronger than the data support: for HD 84937 the 6757 Å line has an equivalent width below 1 mÅ and only a depression is visible, and several cells in Table 2 are empty because of blends, weakness, or missing spectral coverage. Please qualify the claim accordingly.
[Section 6, Table 4] The example grid table contains many blank entries without a legend; please specify whether blanks mean 'correction not computed because equivalent width is below 5 mÅ' or 'outside the computed range', so that users can interpret the electronic grid correctly.
[Section 3, Table 1] Adding a column with the source and estimated uncertainty of each adopted log gf would make the recommended line list more reproducible and would support the authors' statement that the refined values are consistent with the theoretical scatter.
[Section 2] The model description would benefit from a brief justification for including S III and S VI but not S IV and S V, since the ionization balance matters at the 10000 K end of the grid and affects the particle conservation underlying the non-LTE calculations.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-cited H-band gf weakens one cross-check, but the central NLTE validation rests on independent IR-triplet gf and multi-star consistency.

other [Section 5, H-band oscillator strengths paragraph]
"As discussed in detail in Korotin et al. (2020), observed proﬁles for the Sun and the studied stars are better described when using the value log gf = BQZ − 0.12 dex."

The H-band line parameters are imported from the same authors' earlier paper rather than from a new independent measurement or calculation. If that earlier value was itself an empirical fit to the same observed profiles, the optical/H-range abundance agreement in Table 2 is partly built in rather than an independent confirmation. This is a secondary cross-check only: the main claim of model adequacy is supported by the IR triplets, whose gf come from laboratory measurements (Zerne et al. 1997), and by the fact that gf calibrated on the Sun are then applied to stars spanning 4858–9600 K and log g 2.3–4.5, which is a genuine transfer test.

full rationale

The paper is largely self-contained. The solar calibration of the visible-multiplet oscillator strengths (Section 3, e.g., log gf ZB +0.088 for multiplet 6, +0.075 for multiplet 8, +0.113 for multiplet 10) is openly presented as a refinement, not as a prediction, and the solar spectrum is not used as an independent validation of those lines. The central test is the 13-star comparison: fixed solar-calibrated gf are applied to stars of different Teff and log g, and independent IR-triplet lines with measured gf are included; the agreement across lines with very different NLTE corrections is nontrivial. The only minor circularity concern is the H-band gf adopted from Korotin et al. (2020), which is a self-citation and, if that earlier choice was also a fit, makes the H-band optical agreement partially built in. However, this is not load-bearing for the grid or for the IR-triplet conclusions. Therefore the overall circularity is low.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central product is a numerical grid, not a derivation from first principles. Its main free inputs are the chosen microturbulence, empirical oscillator-strength offsets fitted to the Sun, an adopted meteoritic solar abundance, and several approximate collision formulas. No new physical entities are introduced.

free parameters (6)

Microturbulent velocity for correction grid = 2 km/s
The grid is computed with a fixed microturbulent velocity of 2 km/s; the paper notes corrections depend strongly on it, so the grid accuracy for stars with different v_t is limited.
log gf offset for S I multiplet 6 (8694 A) = +0.088 dex relative to ZB
Adjusted so solar synthetic spectra match observed profiles at meteoritic S/H=7.15; not independently measured.
log gf offset for S I multiplet 8 (6743-6757 A) = +0.075 dex relative to ZB
Fitted to the solar spectrum at meteoritic S/H.
log gf offset for S I multiplet 10 (6052 A) = +0.113 dex relative to ZB
Fitted to the solar spectrum at meteoritic S/H.
log gf offset for 15400 A H-band multiplets = BQZ -0.12 dex
Adopted from Korotin et al. 2020 based on observed solar and stellar profiles; not newly measured here.
Effective collision strength for forbidden transitions = 1
Allen (1973) formula with effective collision strength set to 1 for forbidden transitions; a hand-chosen approximation.

assumptions (6)

domain assumption The MULTI statistical-equilibrium and radiative-transfer solution with the described S I/S II/S III model reliably computes level populations.
The paper relies on this to generate b-factors and synthetic profiles; no independent check of the code modifications is shown.
domain assumption Collisional rates from Belyaev & Voronov 2020 (hydrogen) and ADAS/Tayal & Zatsarinny (electrons) are accurate and complete enough for the modeled lines.
These external calculations replace older Drawin formulas; if they have errors, the NLTE corrections inherit them.
domain assumption Solar photospheric sulfur abundance equals the meteoritic value, (S/H)=7.15 +/- 0.02 (Lodders 2021).
Used as the reference for solar line fitting and gf refinement; assumes the Sun is unevolved and its photosphere retains the initial composition.
domain assumption Atmosphere models (ATLAS9 with ODF from Meszaros et al. 2012) and literature stellar parameters for test stars are accurate.
Abundances and validation depend on adopted Teff, logg, [Fe/H], microturbulence, and v sin i from Jofre et al. 2015 and others; no error propagation is made.
ad hoc to paper For higher S I levels not covered by detailed rates, approximate van Regemorter, Allen, and Seaton formulas are adequate.
Most of the 64 S I levels use approximate rates; the paper gives no sensitivity tests for this approximation.
domain assumption Other elements can be treated in LTE in synthetic spectra without affecting S I line fits.
SynthV calculates lines of other elements in LTE while only sulfur uses non-LTE populations; blends and continuum from other elements are assumed correct.

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Cite this review

Pith. "Pith review of Influence of departures from LTE on determinations of the sulfur abundances in A-K type stars." pith.science (2026). https://pith.science/paper/MESXFRD3

@misc{pith2026250100774,
  author       = {Pith},
  title        = {Pith review of: Influence of departures from LTE on determinations of the sulfur abundances in A-K type stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MESXFRD3}},
  note         = {Machine review of arXiv:2501.00774}
}

read the original abstract

The influence of departures from local thermodynamic equilibrium (LTE) on neutral sulfur lines is considered. A grid of corrections is proposed to take into account the influence of departures from LTE for neutral sulfur lines in the visible and infrared spectral regions, including the H-band. The grid is calculated using the atomic model of sulfur incorporating the most up-to-date collision rates with electrons and hydrogen. The inclusion of levels and transitions of ionized sulfur in the atomic model made it possible to expand the range of effective temperatures of stellar photospheres in the grid up to 10000 K. The atomic model was tested in determining the sulfur abundance of 13 stars and showed its adequacy in a wide range of fundamental stellar parameters. In the spectra of all test stars, the sulfur lines are fitted with similar abundances of the element, regardless of the degree of influence of the effects of deviation from LTE on a particular spectral line. For lines of several multiplets, the wavelengths and oscillator strengths were refined. A list of S I lines recommended for determining sulfur abundance has been created.

Figures

Figures reproduced from arXiv: 2501.00774 by the authors.

**Figure 1.** Grotrian diagrams for S I (left) and S II (right). Only transitions used to determine sulfur abundances are shown. ing lines are either too weak or blended. Notably, the eighth and tenth multiplets each consist of three lines, and each line itself is a superposition of three components with slight wavelength shifts. Such line profiles deviate significantly from a Gaussian shape, necessitating synthetic spectrum calc… view at source ↗

**Figure 2.** Distribution of b-factors in the Sun’s atmosphere (left panel) and the variation of the Sl /Bν ratio with depth for two IR triplets (right panel). Arrows indicate the formation depths of some sulfur lines 9227.5 9228.0 9228.5 9237.0 9237.5 9238.0 10455 10456 10457 10458 10459 10460 0.5 0.6 0.7 0.8 0.9 1.0 S I S I S I (A) o S I Relative flux S I [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Comparison of observed (circles) and synthetic profiles of IR triplet lines in the Sun’s spectrum. The non-LTE profile for sulfur abundance (S/H) = 7.16 is shown as a solid line, and the LTE profile, calculated with the same abundance, is shown as a dashed line. same time, oscillator strengths from DH resulted in excessively strong calculated lines. The difference between log gf from DH and ZB is 0.13 dex for all co… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Comparison of observed (circles) and synthetic profiles of the eighth and tenth multiplet lines in the Sun’s spectrum. Profiles with refined parameters are shown as solid lines, and those calculated with VALD parameters are shown as dotted lines [PITH_FULL_IMAGE:figur…

**Figure 5.** Figure 5: Comparison of observed (circles) and synthetic profiles of neutral sulfur lines in the spectra of HD 84937 and t Cet. The non-LTE profile is shown as a solid line, while the LTE profile, calculated with the same abundance, is shown as a dashed line. nearly free from th…

**Figure 6.** Figure 6: Comparison of observed (circles) and synthetic profiles of neutral and ionized sulfur lines in the spectrum of o Peg. The non-LTE profile is shown as a solid line, and the LTE profile, calculated with the same abundance, is shown as a dashed line [PITH_FULL_IMAGE:figu…

**Figure 7.** Figure 7: Non-LTE corrections for metallicity [Fe/H] = 0 Article number, page 8 of 14 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Same as Fig.7 for [Fe/H]=-0.5 Article number, page 9 of 14 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Same as Fig.7 for [Fe/H]=-1.0 Article number, page 10 of 14 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Same as Fig.7 for [Fe/H]=-1.5 Article number, page 11 of 14 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Same as Fig.7 for [Fe/H]=-2.0 Article number, page 12 of 14 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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